μ+ diffusion and trapping in high purity and oxygen-doped Nb

Data are presented for the temperature dependence of the muon depolarization rate between 10 K and 120 K for three samples of niobium of varying. purity. Two samples, each containing approximately 200 ppm substitutional Ta and interstitial concentrations of 10 ppm and 560 ppm (mostly O), respectively, were studied. A third sample containing only 3 ppm Ta and an estimated 10 ppm total interstitial impurities was also measured. The results indicate that even at the lowest temperatures studied the depolarization of the muon is dominated by traps associated with impurities.This work was supported by the U. S. Department of Energy     

Muon diffusion and trapping by defects in electron-irradiated Nb and Ta

The transverse spin relaxation of positive muons ( ⁺) has been measured on Nb and Ta after irradiation with 3 MeV electrons. In high-purity Nb the ⁺ diffusivity derived from the trapping at irradiation-induced defects above 100 K is explained in terms of adiabatic hopping. At lower temperatures there is evidence for the dominating processes to be fewphonon incoherent tunnelling and coherent hopping. Annealing results in the formation of new defects capable of trapping the ⁺. In Ta at least two types of irradiation-induced defects capable of trapping ⁺ survive up to annealing temperatures of 400 K.     

Muon trapping and diffusion in Al and In after electron irradiation at 9 K

The transverse spin relaxation of positive muons has been measured on an Al single crystal and on polycrystalline In after irradiation with 2 MeV electrons at 9 K or 11 K, sample transfer at 4.2 K, and various subsequent annealing treatments. The Al data are analysed in terms of diffusion-limited trapping by vacancies. This yields a muon diffusivityD _μ which within experimental accuracy is proportional toT between 4 K and 50 K, indicating that in this temperature intervalD _μ is dominated by one-phonon-assisted incoherent tunnelling. In In only very small effects due to the irradiation could be observed. The muons appear to be localized in octahedral interstices. From the motional averaging taking place above about 20 K the diffusivity ofD _μ in In is deduced.     

Muon diffusion in metals

The hopping rate W of the positive muon in metals is studied theoretecally. We consider four interactions: muon-electron interaction, linear as well as quadratic muon-lattice interactions and inhomogeneous broadening of the muon levels due to imperfections. The W-vs-T curve consists of four regions. The highest-T region, where the small polaron theory is applicable, is followed by a minimum, below which the Kagan-Klinger damping may be dominant. Then, the damping due to metallic electrons dominates and the hopping rate obeys a power law of a negative power. When kT is smaller than the inhomogeneous broadening, the hopping rate obeys another power law of a positive power, as Sugimoto has shown. We analyze experimental data on muon diffusion in Cu, Al and Fe.     

Muon trapping at substitutional Ti in Fe

Iron doped with 400 ppm Ti was investigated by the muon spin rotation method. Below 70 K and above 180 K the normal 50 MHz signal of pure Fe was observed. However, in a small temperature range around 100 K a completely different frequency with v = 112 MHz shows up. This signal is attributed to muons trapped at Ti in Fe. The experiment yields the hyperfine field B_hf and the binding energy E_B for the trapped muons. We find B_hf = 93(5) mT and E_B = 81(5) MeV.     

Muon diffusion in nanocrystalline copper

A systematic μSR study on nano‐Cu has demonstrated that the diffusion of μ⁺ in nanocrystalline metals is influenced by both features of the nanostructure, i.e., by the very small grain size and by the comparatively large fraction of grain boundaries. The former feature yields a size effect of the phonon‐assisted muon tunneling, but only at particle diameters below 20 nm. The latter feature, in samples with crystallite sizes above 20 nm diameter, i.e., with bulk diffusional behaviour, establishes a connection between μ⁺ diffusion coefficient and particle size: if one of these quantities is known, the other could be evaluated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon trapping at vacancies in pure and doped iron

This paper gives a summary of the results obtained by the Konstanz group on electron-irradiated iron. The main achievement was the observation of a number of different frequencies in Fe, which could be assigned to isolated vacancies and to vacancy-impurity pairs. The annealing behaviour of these frequencies was studied. In the present paper, the framework for the analysis of the data and the main conclusions are reviewed.     

Muon diffusion and level crossing in copper

We have studied the quantum diffusion of positive muons in pure copper over the temperature range 12 mK≤T≤150 K using weak longitudinal field μSR. Below 150 K, this technique has proved to be the most sensitive to the muon hop rate. Our final results for the behaviour of the muon hop rate are well explained within the framework of theories for the quantum diffusion of light interstitials in metals of Kondo, Yamada and others. In addition, the use of level-crossing resonance has allowed us to measure the electric quadrupole interaction strength (and sign) of the copper nuclei, ω_Q= −3.314(7) μS⁻¹. These results have enabled us to show that the muon occupies the same octahedral site at all the temperatures studied, ruling out the possibility of metastable muon sites contributing to any significant portion of the muon polarization.     

Muon spin-lattice relaxation and muonium diffusion in ice

Longitudinal muon spin relaxation is measured in ice, using samples with and without enrichment in H₂ ¹⁷O, with a view to studying the mobility of the muonium fraction. A conventional analysis of the data, on the assumption that relaxation of the diamagnetic fraction is negligible, suggests that more than one mechanism of muonium relaxation is at work. A Bayesian analysis warns that separation of the diamagnetic and paramagnetic signals may not be so straightforward.     

Muon diffusion in copper bolow 2K

Transverse field SR experiments were performed on several different samples of copper in the temperature range below 2K, including isotope separated copper, Fe and Si doped polycrystalline copper and monocrystalline copper. No strong isotope dependent effect was observed. A⁶³Cu and a natural copper sample of identical purity both yield 0.16 s^–1 for the low-temperature plateau, while an increased linewidth inthe⁶⁵Cu case may be related to the strong effects of Fe impurities. Careful transverse field measurements on large single crystals at 0.08K reveal non-Gaussian lineshapes in accordance with the picture of diffusing muons at this temperature. This allows us to reject several of the existing models for muon behaviour in copper below 2K.     

Muon diffusion in Nb−H systems

We have studied the muon diffusion in various Nb−H_X systems with 0.75<x<0.95, with special attention to the concentrations x<0.9. For x>0.9 the muon linewidth as function of temperature has a smooth behaviour and the muon mobility is strongly correlated to the hydrogen diffusion in the beta phase. The activation energy for the μ⁺ diffusion is 160 meV, which is lower than that for protons. At hydrogen concentrations below 0.9, the muon diffusion behaviour is more complicated, and the influence of Nb−H phase transitions is evident. The implications for the local environment of the muon are discussed.     

Muon diffusion in β-V2H

Hydrogen diffusion in the ordered hydride β-V₂H is mainly brought about by a minority fraction of interstitial atoms on antistructural sites. Recently, this mechanism was elucidated in a single crystal QNS study at temperatures close to the critical point (390 K≤T≤440 K) where already an appreciable amount of antistructural sites is occupied. Here we use the positive muon as a radioactive hydrogen tracer in order to show that the same diffusion mechanism is also valid at low temperatures (80 K≤T≤320 K) where the different jump processes are very slow and where the fraction of antistructural atoms is tiny but nevertheless dominates the long range diffusion.     

Magnetoluminescence studies of excitonic scattering processes in high purity GaAs

The broad emission line at about 1.512 eV, which dominates the emission spectra of pure GaAs at intermediate excitation levels (1–300 kW/cm²) and low temperatures (<40 K) is investigated in magnetic fields up to magnetic flux densities of 10 T. The shift of the emission maximum in the magnetic field is exactly the same as recently reported for the free exciton. This demonstrates that at high excitation levels exciton-electron scattering is the dominant mechanism for the radiative decay of free excitons.     

Muon induced fission in high threshold nuclei

Muon captures by nucleon pairs via meson-exchange currents produce a high energy excitation tail in heavy nuclei. The muon induced fission by these excitations is calculated in several subactinide nuclei with high threshold fission barriers. The probability for delayed fission ranges from 4×10^?5 to 4×10^?3 for the isotopes considered.     

Muon studies of organic ferromagnets and conductors

Muon spin rotation (μSR) experiments can be especially helpful in the study of various organic molecular materials. The technique has been used to study the magnetization in nitronyl nitroxide organic ferromagnets, the spin-density-wave ground state in various charge transfer salts, the dynamics of carriers in organic conductors and the vortex structures in organic superconductors. I outline the motivation for studying these new materials and review and discuss the results of recent work.